Problem: Rewrite as a simplified fraction. ${1.7\overline{28} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 1728.2828...\\ 10x &= 17.2828...\end{align*}}$ Subtracting the two equations, we have: ${990x = 1711}$ ${x = \dfrac{1711}{990}} \text{or} {1 \dfrac{721}{990}}$